EXAMPLE 1 Graph a square root function Graph y =,and state the domain and range. Compare the graph with the graph of y =. 1 2  x  x SOLUTION Make a table.

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Presentation transcript:

EXAMPLE 1 Graph a square root function Graph y =,and state the domain and range. Compare the graph with the graph of y =. 1 2  x  x SOLUTION Make a table of values and sketch the graph.

EXAMPLE 1 Graph a square root function The radicand of a square root must be nonnegative. So, the domain is x ≥ 0. The range is y ≥ 0. The graph of y = is a vertical shrink of the graph of y = by a factor of.  x 1 2  x 1 2

EXAMPLE 2 Graph a cube root function Graph y = –3 3, and state the domain and range. Compare the graph with the graph of y =.  x x  3 SOLUTION Make a table of values and sketch the graph.

EXAMPLE 2 Graph a cube root function The domain and range are all real numbers. The graph of y = – 3 is a vertical stretch of the graph of y = by a factor of 3 followed by a reflection in the x- axis. x  3 x  3

EXAMPLE 3 Solve a multi-step problem Use a graphing calculator to graph the model. How long is a pendulum with a period of 3 seconds? Pendulums The period of a pendulum is the time the pendulum takes to complete one back-and-forth swing. The period T (in seconds) can be modeled by T = 1.11 where l is the pendulum’s length (in feet).  l

EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Graph the model. Enter the equation y = The graph is shown below.  x Use the trace feature to find the value of x when y = 3. The graph shows x 7.3. STEP 2

EXAMPLE 3 Solve a multi-step problem ANSWER A pendulum with a period of 3 seconds is about 7.3 feet long.

GUIDED PRACTICE for Examples 1, 2 and 3 1.y = – 3 x  SOLUTION ANSWER Domain:Range: x > 0 y < 0 Make a table of values and sketch the graph.

GUIDED PRACTICE for Examples 1, 2 and 3 SOLUTION ANSWER Domain:Range: x > 0 y < 0 2. y = 1 4  x Make a table of values and sketch the graph. x1234 y

GUIDED PRACTICE for Examples 1, 2 and 3 3. y =  x – ANSWER Domain:Range:All real numbers x y SOLUTION Make a table of values and sketch the graph.

GUIDED PRACTICE for Examples 1, 2 and 3 4.g(x) = 4 x  3 ANSWER Domain:Range:All real numbers x y SOLUTION Make a table of values and sketch the graph.

GUIDED PRACTICE for Examples 1, 2 and 3 5. What if ? Use the model in example 3 to find the length of a pendulum with a period of 1 second. ANSWER About 0.8 ft